The global Positioning System (GPS), also called NAVSTAR, consists of a plurality of GPS satellites. The orbits of the GPS satellites are arranged in multiple planes, in order that signals can be received from at least four GPS satellites at any point on or near the earth. The satellite transmissions are controlled and accurately synchronized by ground stations; and the receiver can measure the range of each satellite from the timing of the received code, which is derived from the received RF signals. The orbital parameters of the GPS satellites are determined with a high degree of accuracy from fixed ground stations and are relayed to the user through the GPS downlink signals. In navigation applications of GPS, the latitude, longitude, and altitude of any point close to the earth can be calculated from the times of propagation of the electromagnetic signals from four or more of the spacecraft to the unknown location. A measured range, known as "pseudorange", between the GPS receiver at the unknown location and the four satellites within view is determined based on these propagation times. The measured range is referred to as pseudorange because there is generally a time difference or offset between timing clocks on the satellites and the GPS receiver clock. Thus, for three dimensional position determinations, at least four satellite signals are needed to solve for four unknowns, i.e., the time offset together with the three dimensional positions of the satellites.
Each GPS satellite transmits two spread-spectrum signals in L band, known as L1 and L2 with separate carrier frequencies at 1575.42 and 1227.6 MHZ, respectively. Two signals, each with a different center frequency, are required in order to eliminate errors that arise due to delays of the satellite signals through the ionosphere. Since the ionospheric delay is inversely proportional to the square of the carrier frequency, the ionospheric delay can be estimated and removed through pseudorange measurements on both L1 and L2 frequencies.
The satellite signals are modulated by two pseudorandom codes: one referred to as the coarse acquisition (C/A) code and the other referred to as the precision (P) code. Both codes are unique to each satellite. This allows the L-Band signals from the plurality of GPS satellites to be individually identified and separately processed in a receiver. The P-code has a 10.23 MHZ clock rate and is used to modulate the L1 quadrature phase and L1 inphase carriers generated within the satellite. The P-code repeats approximately once every week. In addition, the L1 signal of each satellite includes an inphase carrier modulated by the C/A code, which has a 1.023 MHZ chip rate and repeats every 1 millisecond. The C/A code carrier and the P-code carrier are in phase quadrature with respect to each other. Each carrier is also modulated by a slowly varying 50 bits-per-second data stream, defining the satellite ephemeris, satellite clock corrections, and other GPS information.
In the GPS receiver, the signals corresponding to the known P-code and C/A code may be generated in the same format as in the satellite. The L1 and L2 signals from a given satellite are demodulated by aligning the phases, i.e., adjusting the timing, of the locally generated codes with the satellite signal. To achieve time alignment the locally generated code replicas are correlated with the received signal until the resultant correlation output is maximized. Since the time at which each code chip is transmitted from the satellite is defined, the time of receipt of a particular chip can be used as a measure of the transit time or range to the satellite. Since the C/A and P-codes are unique to each satellite, a specific satellite may be identified based on the results of correlations between the received signals and the locally generated C/A and P-code replicas.
Since the C/A code has a short repetition cycle (1 millisecond), C/A code acquisition can be accomplished rapidly without knowledge of GPS time, which is related the code state of the transmitted signal at the time of signal acquisition. Accordingly, acquisition of the PDC code is generally accomplished by first acquiring the C/A code signal, since there exists a predefined timing relationship between the C/A code and the P-code unique to each satellite. This timing relationship is given in the Hand-Over-Word (HOW) in the navigation message of the C/A code signal. Once the C/A code is acquired, L1 carrier demodulation of the L1 signal can be accomplished with suppressed carrier demodulation techniques such as the Costas loop. If extreme accuracy in the quantity being measured by the receiver is not required, use of the L1 carrier alone may allow satisfactory "carrier wave measurements". However, in kinematic applications, when high-resolution carrier-wave measurements are desired to be made or when measurements are desired to be made quickly, the L2 carrier signal also can be utilized. The use of both L1 and L2 carrier phase is desired for carrier phase ionospheric delay estimation and removal. The availability of both L1 and L2 carriers allow the formation of the so-called "widelane" frequency that is the difference frequency between L1 and L2 and is useful for rapid carrier phase ambiguity resolution.
Kinematic or carrier-phase differential techniques are a natural outcome of the use of GPS for surveying applications. Rather than making use of the code measurements that can be adversely affected by multipath (signal reflections), the reconstructed carrier-phase measurements are used in surveying and kinematic applications. The high accuracy that can be obtained from carrier-phase measurements is related to the relative wavelengths involved. The "chip" rate of the C/A code has a wavelength of approximately 300 meters. The corresponding "chip" rate of the P code has a wavelength of approximately 30 meters. The wavelength of the L1 carrier is 19 cm, and the wavelength of the L2 carrier 24.4 cm. A common rule of thumb is that a measurement can be made to a precision that is about 1/40th of the wavelength. Thus, a carrier-phase measurement can be obtained that is much more accurate than the code measurements. However, the carrier-phase measurement has one very significant disadvantage compared to the code measurements. Specifically, the carrier-phase measurement can be used as an accurate range measurement only if the correct number of whole cycles of the carrier signal in transit between the satellite and the receiver can be determined in some manner. An equivalent requirement for use in a differential application is to determine the difference in the number of whole cycles at the reference receiver and the kinematic receiver. The source of the problem is that each cycle of the carrier signal is identical and it is not obvious when the particular cycle being received was transmitted from the satellite.
Several methods of determining the cycle ambiguity have been developed. The first method used in surveying applications was simply to collect a sufficient amount of data while stationary so that the change in carrier phase (integrated Doppler) could be used to compute a position in three dimensions that would be accurate to at least one half a wavelength. Thus, if L1 carrier phase measurements were being used, the integrated Doppler position would need to be accurate to 9.5 centimeters in each of the three dimensions. Once the desired accuracy is achieved, the computed range to the satellite can be used to resolve the whole-cycle ambiguity value. Once the whole-cycle ambiguity values are set, the position can be recomputed. Typically, this revised solution results in differential positions accurate to less than one centimeter.
Recently, other more sophisticated methods have been developed and used to resolve the whole-cycle ambiguities in the carrier-phase measurements for the moving or "kinematic" receiver. Like the survey applications, they depend upon a static reference receiver that is used to measure the systematic errors in the code and carrier measurements and transmit them in real time to the kinematic receiver. Typically, these ambiguity-resolution methods make use of both the code and carrier measurements in a multi step process. First, the code measurements are used to obtain a differential position whose accuracy is on the order of 1 to 5 meters. Next, an uncertainty region or volume of space is defined around the code differential position that has a high probability of containing the true solution. Finally, combinations of whole-cycle ambiguity values are chosen for each carrier-phase measurement such that the resultant carrier-phase solution both (1) lies within the uncertainty volume and (2) has a small RMS residual. The requirement of a small RMS residual means that measurements to at least five satellites are required because at least one redundant measurement is needed in order to compute residuals. If more than one combination of whole-cycle ambiguity values meets the requirements, the process is repeated with the next set of measurements. The motion of the satellites ensures that the residuals will grow on any solution that is not correct. Only the one true solution should continue to yield small RMS residuals as the satellites move.
Two elements of the above description show a significant advantage accrues with the use of longer carrier wavelengths. First, the number of combinations of whole-cycle ambiguities that will have solutions within any given uncertainty volume decreases as the cube of the wavelength involved increases. Second, the closer a false solution is to the true position, the greater the amount of satellite motion is required to cause the residuals of that solution to grow an equal amount. Both of these factors favor the use of the L2 carrier over the L1 carrier since the L2 wavelength is almost 30 percent longer than the L1 wavelength. However, the major motivation to obtain L2 carrier-phase measurements arises for another reason. Specifically, the difference measurements obtained by subtracting the L2 carrier-phase measurements from the L1 measurements have a wavelength of 86 centimeters that corresponds to the wavelength of the difference frequency of L1 minus L2. This wavelength is 4.5 times longer than the L1 wavelength and means that there will be approximately (4.5).sup.3 or about 100 times fewer combinations of whole-cycle ambiguities positioned within the same uncertainty volume. Furthermore, the required satellite motion needed to cause the RMS residuals to exceed the elimination threshold will be at least 4.5 times smaller. In summary, there is a very large benefit to the whole-cycle ambiguity resolution process when carrier-phase measurements can be obtained on the L2 carrier.
Although both the C/A and P-code unique to each satellite are known, each satellite is provided with the capability of modulating its P-code with a secret anti-spoofing (A/S) code prescribed by the United States Government. This secret code is intended to prevent a terrorist or enemy from generating a signal simulated to appear as a signal transmitted from a GPS satellite that could be used to "spoof" or fool a GPS receiver into computing a false position. A security code, the W code not available to civilian users, is modulo-2 added with the P codes on both L1 and L2 signals, thereby encrypting the L1 and L2 P-code signals. Since the W-code is not publicly known it will provide the anti-spoofing function and protect military users from interpreting enemy signals, which may be identical to the publicly known P-code, as valid satellite signals. When this A/S modulation is employed, the combination of P-code with W-code is referred to as the Y-code. From measurements using high gain dish antennas, it has been empirically determined that the W-code chip rate is approximately 500 KHz, or roughly 1/20.sup.th of the P-code chip rate.
Since L2, unlike L1, has the P-code component only, its access is denied to all users without knowledge of the W-code. This has severe impacts to survey users and carrier phase differential (or kinematic) users whose achievable accuracy will be degraded since dual frequency ionospheric delay correction cannot be obtained without the L2 signal, and rapid carrier phase ambiguity resolution cannot be implemented with developed techniques using the difference frequency between L1 and L2 (the widelane Frequency) that has a wavelength that is 4.5 times larger than L1.
While the L1 signal includes a quadrature phase carrier modulated by the P-code and an inphase carrier modulated by the C/A code, the L2 signal is only modulated by the P code. Accordingly, when the A/S code is employed a standard receiver with no access to the Y-code would not be able to recover the L2 code and carrier phase information with standard correlation techniques. This loss of access to the L2 signal presents two distinct problems to some user groups. First, it means that there is no means to measure and correct for the ionospheric refraction effects on the pseudorange measurements. More significantly, it can be a serious problem to the survey user and the carrier-phase differential or "kinematic" user, both of whom desire to achieve accuracies below 1 centimeter, because they would not be able to demodulate the L2 carrier phase reliably and accurately without knowledge of the classified Y-code.
The large benefit from L2 carrier-phase measurements has resulted in the development of several methods for obtaining the required L2 carrier phase measurements even in the event that the A/S code is turned on, i.e., when the P-code is encrypted to become Y-code, and access by nonmilitary users to the L2 signal is denied. A number of techniques have been suggested for obtaining the L2 carrier phase even in the presence of the A/S code encryption.
In the first technique described by Ashjaee et al (U.S. Pat. No. 4,928,106) the received L2 signal is multiplied by itself, or squared, in order to remove its biphase data modulation imposed by the secret W-code. The squaring process generates a single-frequency output signal, the phase of which can be measured when A/S is turned on. However, there are two significant disadvantages of the squaring process. First, the output frequency is twice the original carrier frequency and, hence, the wavelength is half of the L2 carrier. Such a reduction in wavelength increases the number of whole cycle ambiguities in carrier wave measurements. The second, even more serious, disadvantage is that the squaring process must be performed in a bandwidth broad enough to include most of the spread-spectrum energy of the incoming signal (.about.20 MHZ). This admits significantly more noise energy into the receiver, thereby significantly degrading the signal-to-noise ratio relative to techniques of carrier recovery relying on a direct correlation process.
In a second technique, commonly known as cross-correlation, the incident L2 signal is multiplied by the L1 signal rather than being squared. Thus, the wavelength is not cut in half as it is in the squaring process. When the L1 and L2 signals are transmitted from the satellite, the P-code modulation of the two signals is synchronized. However, the ionospheric refraction causes a longer delay in the L2 signal than in the L1 signal. Thus, in order to maximize the signal, the L1 signal must be delayed by a variable amount in order to align the P code modulation of the two signals. Since the cross-correlation must still be done in the spread spectrum bandwidth, significant degradation remains. The degradation is somewhat less, however, as a consequence of the increased transmitted energy in the L1 signal relative to the L2 signal.
A third technique, known as P code aided squaring, is described by Keegan (U.S. Pat. No. 4,972,431) to reduce the signal to noise ratio degradation inherent in the techniques described above. Because the Y-code is a composite of both P-code and W-code modulation, it is possible to remove the P-code component of the received signal and reduce its bandwidth to that of the W-code by multiplying it with a locally generated replica of the P code and filter the product signal to the W-code bandwidth of approximately +/-500 KHz. The local P-code phase is adjusted until a strong demodulated signal appears at the filter output. The narrower bandwidth signal is squared to remove the W-code modulation for carrier recovery. Although leading to an improved signal to noise ratio (SNR) as compared to the squaring and cross-correlation techniques described above, this technique results in a doubling of the L2 frequency in the squaring process, thereby reducing the observable wavelength by one half. Again, such a wavelength reduction results in a commensurate increase in the number of whole cycle ambiguities to be resolved. In addition, filtering of the product signal of L2 and the local P-code is performed by an analog bandpass filter, which is not the optimal filter for the W-code signal. The optimal filter will be an integrate-and-dump filter over the W-code bit time if the W-code timing is available. This performance of this technique is thus not the optimal achievable.
In a fourth technique for obtaining the L2 carrier phase in the presence of the A/S code encryption, described by Lorenz et al. (U.S. Pat. No. 5,134,407), the L1 and L2 signals are initially correlated with locally generated P-code and carrier signals. The resultant signals are then integrated for a duration estimated to be the period of the classified W-code. The W-bit period varies and is approximately 20 or 22 P-chips in duration. The W-bit timing relationship is related to the P-code phase and can be observed from a GPS downlink using a high gain antenna even though the W-bit data is not publicly known. Based on these integration processes separate estimates are made of the unknown W-code on a bit-by-bit basis. In a particular embodiment an estimated W-bit polarity obtained on the L2 channel is cross correlated with the L1 signal after decorrelation is performed using the local P-code replica. The resultant L1 signal can then be coherently code tracked. Similarly, an estimated polarity of the W-code bit obtained on the L1 channel is cross correlated with the L2 signal after decorrelation using the local P-code replica. Full wavelength carrier tracking can then be performed on the resultant L2 signal since the modulation of the unknown W-code is removed in the cross-correlation process. Although allowing for an improved SNR relative to other methods of L2 carrier recovery, the method described by Lorenz does not yield optimal accuracy as a consequence of the "hard decision" made in estimating the values for the individual W-code bits. That is, each bit is specifically determined to be one of two binary values by comparing the results of each integration process with a predefined threshold, thereby resulting in less than optimal SNR.
In a fifth technique, described by Litton, Russell and Woo (U.S. Pat. No. 5,576,715), an optimal processing technique for L2 demodulation is derived based on Maximum A Posteriori estimation of the L1 W-bits on a bit-by-bit basis, combined with corresponding estimation of the L2 W-bits. This further improves the signal-to-noise performance of the technique described by Lorenz et al. In a particular embodiment, the band limited L2 signal, after correlation with the punctual P-code generated by the P-code generator in the L2 channel, is mixed with the local carrier reference to produce the inphase and quadrature signals proportional to cos (.phi.) and sin (.phi.), respectively, where .phi. represents the phase difference between the received L2 signal and a locally generated replica thereof. The inphase and quadrature channels are integrated over an integration period that approximates the W-bit period. Each estimate of a W-code bit on the inphase, i.e., the cosine channel, is combined with the hyperbolic tangent of a corresponding L1 channel W-code bit estimate, weighted by the factor 1.4142, which is selected to compensate for the greater signal strength (.about.3 dB) of the received L1 signal relative to the received L2 signal. The resultant sum is multiplied with the L2 quadrature (i.e., sine) channel integrated over the corresponding W-code bit period to obtain an estimate of L2 carrier phase error. The resulting carrier phase error estimate is used to adjust the locally generated L2 carrier phase. The phase error estimate consists of two components: one component proportional to sin (.phi.) that results from multiplying the hyperbolic tangent of the L1 W-bit estimate with the L2 inphase channel integrate and dump output, and the second component proportional to sin (2.phi.) that results from multiplying the L2 inphase channel integrate and dump output with the L2 quadrature channel integrate and dump output. The addition of the component that is proportional to sin (.phi.) allows full-wavelength carrier recovery and prevents the locally generated L2 carrier from becoming locked one-half carrier cycle out of phase with the received L2 carrier.
In both techniques described by Lorenz et al. and by Litton et al. estimation of the unknown W-code bits is performed on a bit-by-bit basis. The W-code bit estimates, used to derive the L2 carrier phase error, are performed at a rate of 500 KHz approximately. Since the W-code bit periods are relatively short (.about.2 microseconds), the SNR of the W-code bit estimates is very low, e.g., -17 dB for a received C/No of 40 dB-Hz. This results in significant degradation in L2 carrier recovery performance as compared to what is achievable when there is no A/S W-code modulation.